Computational and Applied Mathematics

, Volume 33, Issue 1, pp 193–202 | Cite as

Group analysis of the Novikov equation

  • Yuri Bozhkov
  • Igor Leite FreireEmail author
  • Nail H. Ibragimov


We find the Lie point symmetries of the Novikov equation and demonstrate that it is strictly self-adjoint. Using the self-adjointness and the recent technique for constructing conserved vectors associated with symmetries of differential equations, we find the conservation law corresponding to the dilation symmetry and show that other symmetries do not provide nontrivial conservation laws. Then we investigate the invariant solutions.


Novikov equation Lie symmetries Strictly self-adjointness  Conservation laws Invariant solutions 

Mathematics Subject Classification (2000)

76M60 58J70 35A30 70G65 



The authors would like to thank FAPESP, São Paulo, Brasil, and BTH, Sweden, for the support giving Nail H. Ibragimov the opportunity to visit IMECC-UNICAMP, where this work was initiated. Yuri Bozhkov would also like to thank FAPESP and CNPq, Brasil, for partial financial support. Igor Leite Freire is thankful to IMECC-UNICAMP for gracious hospitality, UFABC and FAPESP (Grant No. 2011/19089-6) for the financial supports. N. H. Ibragimov’s work is partially supported by the Government of Russian Federation through Resolution No. 220, Agreement No. 11.G34.31.0042.


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Copyright information

© SBMAC - Sociedade Brasileira de Matemática Aplicada e Computacional 2013

Authors and Affiliations

  • Yuri Bozhkov
    • 1
  • Igor Leite Freire
    • 2
    Email author
  • Nail H. Ibragimov
    • 3
    • 4
  1. 1.Instituto de Matemática, Estatística e Computação Científica-IMECCUniversidade Estadual de Campinas-UNICAMPCampinasBrasil
  2. 2.Centro de Matemática, Computação e CogniçãoUniversidade Federal do ABC-UFABCSanto AndréBrasil
  3. 3.Laboratory “Group Analysis of Mathematical Models in Natural and Engineering Sciences”Ufa State Aviation Technical UniversityUfaRussia
  4. 4.Department of Mathematics and ScienceBlekinge Institute of TechnologyKarlskronaSweden

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